Slope and Systems

Presentation

•

Mathematics

•

9th Grade

•

Hard

Joseph Anderson

FREE Resource

4 Slides • 26 Questions

Yay!!

Systems Practice!

Let's convert to slope-intercept form

2y = x - 5

Let's convert from standard to slope-intercept form

-3x + 6y = -15

Multiple Choice

What is the first step to convert this equation into slope-intercept (y=mx+b) form?

8x - 2y = 22

Subtract 8x from both sides

Subtract 2y from both sides

Divide by 8

Divide by -2

Multiple Choice

What is the correct way to subtract 8x from both sides?

8x - 2y = 22

-2y = 14x

-2y = 12x

-2y = 22 - 8x

-2y = 12 - 8x

Multiple Choice

What is the next step to convert the equation into slope-intercept (y=mx+b) form?

-2y = 22 - 8x

Divide by -8

Divide by -2

Multiply by -2

Multiply by -8

Multiple Choice

After you divide this equation by -2, what will it become?

-2y = 22 - 8x

-y = -11 -4x

y = -11 + 4x

-y = -11 + 4x

y = -11 - 4x

Math Response

What is the y-intercept of this equation?

y = -11 + 4x

Type answer here

Deg^°

Rad

Math Response

What is the slope of this equation?

y = -11 + 4x

Type answer here

Deg^°

Rad

Multiple Choice

If the slope is 4, what does that mean for how we would graph it?

Starting at the y-intercept, go up 4 and left 1

Starting at the y-intercept, go down 4 and left 1

Starting at the y-intercept, go up 4 and right 1

Starting at the y-intercept, go down 4 and right 1

Graphing

Please graph this equation:

y = -8 + 4x

(Note: this is a different equation from the one we've been using because the previous one doesn't fit on this graph)

Which of these are solutions for
-8y > 32x -8?

(0, 0)
(1, -3)
(-2, 10)

Multiple Choice

What is 4y < 16x - 4 in slope-intercept form?

y < 4x - 1

y > 4x - 1

y < 4x + 1

y > 4x +1

Multiple Select

Now that we have the inequality y < 4x - 1, which of these points are solutions to the inequality?

(0, -1)

(1, 4)

(0, -2)

(1, -4)

Hotspot

Where is the y-intercept of the red line?

Hotspot

Where is the zero of the red line?

Hotspot

Where is the y-intercept of the blue line?

Hotspot

Where is the zero of the blue line?

Drag and Drop

Let's find the rate of change with respect to x (slope) of the blue line. Remember, slope is the change in y (rise) divided by the change in x (run). For the blue line, the change in y (rise, or how much it goes up between points) is

and the change in x (run, or how much it moves to the right between points) is

. So, the total rate of change with respect to x (slope, change in y divided by change in x) is

Drag these tiles and drop them in the correct blank above

-0.5

-2

-1

-5

-7

0.5

Drag and Drop

Let's find the rate of change with respect to x (slope) of the red line. Remember, slope is the change in y (rise) divided by the change in x (run). For the red line, the change in y (rise, or how much it goes up between points) is

and the change in x (run, or how much it moves to the right between points) is

. So, the total rate of change with respect to x (slope, change in y divided by change in x) is

Drag these tiles and drop them in the correct blank above

-0.5

-2

-1

-5

-7

0.5

Open Ended

If the slope of the blue line is 2 and its y-intercept is 1, please write the equation of the blue line.

Type response here

Open Ended

If the slope of the red line is -1 and its y-intercept is 7, please write the equation of the blue line.

Type response here

Hotspot

Where is the solution of this system of equations?

Fill in the Blanks

Using Desmos, what is the solution to this system of equations?

y = (1/4)x + 5

y = -4x + 5

Fill in the Blanks

Using Desmos, what is the solution to this system of equations?

2y = 8x + 4

y = x + 5

(Hint: get y by itself in the first equation)

Fill in the Blanks

Using Desmos, what is the solution to this system of equations?

-4y = 12x + 24

y = (1/2)x + 43

(Hint: get y by itself in the first equation)

Math Response

We can find slope from a table, too. Just like with a graph, we'll look for the change in y and the change in x. If x is the time in hours, what is the change in x between the first two points?

Type answer here

Deg^°

Rad

Math Response

If y is the number of meals packed, what is the change in y between the first two points?

Type answer here

Deg^°

Rad

Math Response

If slope is the change in y (125, the number of meals packed) divided by the change in x (1, the number of hours), what is the rate of change with respect to x (slope) shown in the table?

Type answer here

Deg^°

Rad

Math Response

In the last question, we found the rate of change with respect to x between the first two points (rows). Now let's look at the last two rows. What is the rate of change with respect to x (slope) shown for these two points (4, 500) and (8, 1000)?

Remember, slope is still *change in y* divided by *change in x*.

Type answer here

Deg^°

Rad

Yay!!

Systems Practice!

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